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Tables of Integrals, Series, and Products

Daniel Zwillinger, I. S. Gradshteyn, and I. M. Ryzhik
Academic Press
Publication Date: 
Number of Pages: 
Hardcover with CDROM
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Allen Stenger
, on

This is a new revision of the indispensable table of integrals. It is not drastically different from the previous edition. (See our detailed review of the 2007 seventh edition.)

This edition omits six short chapters from the previous edition that dealt with items outside the main stream of the book (the omitted chapters are Algebraic Inequalities, Matrices, Determinants, Norms, Ordinary Differential Equations, and Z-Transforms). I never got much value out of these chapters, mostly because they’re skimpy and have much less detail than is found in more specialized references. I won’t miss these. This deletion amounts to about 48 pages of material. The two editions have the same formatting, and the body of the new book is 37 pages shorter (1140 vs. 1103 pages), so there’s a net gain of 11 pages in new retained material.

The publisher’s web site claims “25% of new material not including changes to the restrictions on results that revise the range of validity of results, which lend [sic] to approximately 35% of new updates” but this estimate seems high. Based on a small random sample of the pages, I estimate about 3% changes (mostly correction of typographical errors) and 4% new material. Still, in a book this size that’s a lot of individual changes, and if you use this book frequently it’s definitely worth getting the new edition, especially because so many typographical errors are corrected. Such errors are hard to detect, and it’s easy to go astray when you’re using the formulas in your work.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.

1 Elementary Functions
2 Indefinite Integrals of Elementary Functions
3 Definite Integrals of Elementary Functions
4 Combinations Involving Trigonometric and Hyperbolic Functions and Power
5 Indefinite Integrals of Special Functions
6 Definite Integrals of Special Functions
7 Associated Legendre Functions
8 Special Functions
9 Hypergeometric Functions
10 Vector Field Theory
11 Algebraic Inequalities
12 Integral Inequalities
13 Matrices and Related Result
14 Determinants
15 Norms
16 Ordinary Differential Equations
17 Fourier, Laplace, and Mellin Transforms
18 The Z-transform